A certain dielectric, with adielectric constant 23...

A certain dielectric, with adielectric constant 23, can withstand an electric field of 5*10^7 V/m. Suppose we want to use thisdielectric to construct a 0.3 ? F capacitor thatcan withstand a potential difference of 2400 V. The permittivity offree space is 8.85 * 10^-12 C^2 /N * m^2.

1. What is the minimum plate separation? Answer in units of? m.

2. What must the area of the plates be?Answer in units of m^2.

Answers ( 1 )

  1. mar ortiz
    mar ortiz
    The capacitance of the capacitor that is to be constructedis C=0.3 ? F
    This could be withstand a potential difference V=2400V
    ?The charge that can store is Q=CxV
                                                     =0.3x10-6 x 2400
                                                     =720x10-6 coulombs  
    But we can have E =Q/(k? 0 A )   fromGauss' law  
                            ?A=Q/kE? 0                             =720x10-6/ (23 x 5x107 x 8.85 x 10-12)
                               =0.707 x 10 -1
                              =0.0707 m2
    Now we have C=k? 0 A/d
                      ?d=k? 0 A/C
        
                           =23 x 8.85 x 10 -12 x .0707 / (0.3x10-6 )
                            =47.96x10-6m  
                            =47.96  ?m
    Therefore the minimum platesepatation should be 47.96  ? m
                    

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